14 found
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  1. Decidability of ∀*∀‐Sentences in Membership Theories.Eugenio G. Omodeo, Franco Parlamento & Alberto Policriti - 1996 - Mathematical Logic Quarterly 42 (1):41-58.
    The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.
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  2.  13
    The Decision Problem for Restricted Universal Quantification in Set Theory and the Axiom of Foundation.Franco Parlamento & Alberto Policriti - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):143-156.
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  3.  9
    Decidability Results for Metric and Layered Temporal Logics.Angelo Montanari & Alberto Policriti - 1996 - Notre Dame Journal of Formal Logic 37 (2):260-282.
    We study the decidability problem for metric and layered temporal logics. The logics we consider are suitable to model time granularity in various contexts, and they allow one to build granular temporal models by referring to the "natural scale" in any component of the model and by properly constraining the interactions between differently-grained components. A monadic second-order language combining operators such as temporal contextualization and projection, together with the usual displacement operator of metric temporal logics, is considered, and the theory (...)
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  4.  16
    Modal Deduction in Second-Order Logic and Set Theory - II.Johan van Benthem, Giovanna D'Agostino, Angelo Montanari & Alberto Policriti - 1998 - Studia Logica 60 (3):387-420.
    In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor (...)
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  5.  11
    Comparing Expressiveness of Set Constructor Symbols.Agostino Dovier, Carla Piazza & Alberto Policriti - 2000 - In Dov M. Gabbay & Maarten de Rijke (eds.), Frontiers of Combining Systems. Research Studies Press. pp. 275--289.
  6.  9
    The Axiom of Elementary Sets on the Edge of Peircean Expressibility.Andrea Formisano, Eugenio G. Omodeo & Alberto Policriti - 2005 - Journal of Symbolic Logic 70 (3):953 - 968.
    Being able to state the principles which lie deepest in the foundations of mathematics by sentences in three variables is crucially important for a satisfactory equational rendering of set theories along the lines proposed by Alfred Tarski and Steven Givant in their monograph of 1987. The main achievement of this paper is the proof that the 'kernel' set theory whose postulates are extensionality. (E), and single-element adjunction and removal. (W) and (L), cannot be axiomatized by means of three-variable sentences. This (...)
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  7.  4
    Foreword.Ewa Orlowska, Alberto Policriti & Andrzej Szalas - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):249-250.
  8.  15
    Expressing Infinity Without Foundation.Franco Parlamento & Alberto Policriti - 1991 - Journal of Symbolic Logic 56 (4):1230-1235.
    The axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed.
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  9.  6
    The Bernays-Schönfinkel-Ramsey Class for Set Theory: Semidecidability.Eugenio Omodeo & Alberto Policriti - 2010 - Journal of Symbolic Logic 75 (2):459-480.
    As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀* -sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for (...)
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  10.  2
    Review: Peter Ohrstrom, Per F. V. Hasle, Temporal Logic. From Ancient Ideas to Artificial Intelligence. [REVIEW]Angelo Montanari & Alberto Policriti - 1997 - Journal of Symbolic Logic 62 (3):1044-1046.
  11.  2
    The Decision Problem for Restricted Universal Quantification in Set Theory and the Axiom of Foundation.Franco Parlamento & Alberto Policriti - 1992 - Mathematical Logic Quarterly 38 (1):143-156.
    The still unsettled decision problem for the restricted purely universal formulae 0-formulae) of the first order set-theoretic language based over =, ∈ is discussed in relation with the adoption or rejection of the axiom of foundation. Assuming the axiom of foundation, the related finite set-satisfiability problem for the very significant subclass of the 0-formulae consisting of the formulae involving only nested variables of level 1 is proved to be semidecidable on the ground of a reflection property over the hereditarily finite (...)
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  12.  4
    Modal Deduction in Second-Order Logic and Set Theory: II.Johan Van Benthem, Giovanna D'Agostino, Angelo Montanari & Alberto Policriti - 1998 - Studia Logica 60 (3):387 - 420.
    In this paper, we generalize the set-theoretic translation method for polymodal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor (...)
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  13.  1
    The Bernays—Schönfinkel—Ramsey Class for Set Theory: Decidability.Alberto Policriti & Eugenio Omodeo - 2012 - Journal of Symbolic Logic 77 (3):896-918.
    As proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shönfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.
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  14. Peter Øhrstrøm and Per F. V. Hasle. Temporal Logic. From Ancient Ideas to Artificial Intelligence. Studies in Linguistics and Philosophy, Vol. 57. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1995, Viii + 413 Pp. [REVIEW]Angelo Montanari & Alberto Policriti - 1997 - Journal of Symbolic Logic 62 (3):1044-1046.